The following is content drawn from 30 Philosophers but adds Pythagoras as an example to the discussion. Read chapter 22 for a more in depth exploration.
Introduction
Pythagoras is a fascinating case study in both sound and flawed thinking. On one hand, his mathematical insights—particularly in geometry and harmonics—were rooted in empirical observation and logical reasoning. On the other hand, his mystical interpretations and rigid numerical dogmatism led him astray. Of interest to us here on pragmatism is that he serves as a prime example of how most people approach truth—through a pragmatic lens.
Pragmatism

At its core, Pragmatism values practical application over intellectual accuracy. William James, a key figure in shaping this tradition, famously stated in his 1907 book, Pragmatism: A New Name for Some Old Ways of Thinking:
The pragmatic method is primarily a method of settling metaphysical disputes…and disputes over such notions are unending. … What difference would it practically make to anyone if this notion rather than that notion were true? If no practical difference whatever can be traced, then the alternatives mean practically the same thing, and all dispute is idle.
This tradition emerged in the United States during the late 19th century and argues that the validity or worth of an idea is determined by its tangible impact. In other words, if an idea works well in practice, then it holds merit. Nearly everyone is pragmatic to some degree—whether they realize it or not. Most of us assign different levels of practical value to beliefs, adhering to the core tenets of traditional Pragmatism in our everyday lives.

Pragmatism and Pythagoras
Pythagoras exemplifies the three types of pragmatism introduced in chapter 22 of 30 Philosophers: empirical, rational, and irrational pragmatism.

Pythagoras as a Rational Pragmatist
Pythagoras’ belief system often overpowered his science, yet his empirical observations stood the test of time. This makes him a rational pragmatist—someone who accepts empirical truths but also accommodates personal beliefs, sometimes at the cost of reason. Unfortunately for his reputation, many of his personal beliefs were very wrong.
Most people fall into this category. They embrace empirical and rational ideas but also accommodate some faith-based beliefs. These beliefs might be spiritual, religious, or simply personal convictions. Rational pragmatists, like Pythagoras, can contribute meaningful advancements while still holding onto ideas that don’t withstand scrutiny—such as Pythagoras’ mystical belief in numbers as divine entities governing reality.
The Empirical Pragmatist: Seeking Only What Is Testable
In contrast, an empirical pragmatist rejects all irrational beliefs and follows empirical and rational truths alone. This mindset aligns with the modern scientific method—trusting only what can be tested and verified. An empirical pragmatist does not mix in personal belief systems that lack supporting evidence.
If Pythagoras had been an empirical pragmatist, he would have discarded his mystical numerology when faced with counter-evidence. Instead, he maintained his belief in the supernatural significance of numbers despite the lack of empirical support.
The Irrational Pragmatist: Dismissing Evidence Altogether
Finally, you can contrast empirical and rational pragmatists with the irrational pragmatist who fundamentally does not believe in a core set of common truths. They reject the notion that empirical and rational truths form the basis for understanding. Unlike most people, who still value empirical evidence, the irrational pragmatist adopts a relativistic perspective. Phrases like “truth isn’t truth” or “everyone has their own truth” often punctuate their dialogue.
Unlike rational pragmatists, who blend empirical thinking with faith-based beliefs, irrational pragmatists disregard evidence altogether. Instead, they embrace disproven or untestable ideas simply because they find them appealing or useful. Whereas Pythagoras at least engaged in some empirical reasoning, an irrational pragmatist would reject the need for evidence entirely, favoring intuition or personal truth over objective reality.
Pythagoras and the Nature of Intellectual Progress
The mathematical insights of Pythagoras—particularly in geometry and harmonics—were rooted in empirical observation and logical reasoning. Yet, he also fathered a major pseudoscience, believing in many disproven ideas. But here’s the key insight: before any idea can be tested, someone has to think it up.
Pythagoras may have been both a brilliant mathematician and the founder of numerological mysticism, but that’s the nature of intellectual progress. Some ideas survive the test of time—others crumble under it.
This perspective highlights why rational pragmatism is the most common approach. Unlike empirical pragmatists, who reject all unsupported beliefs, most people—like Pythagoras—blend reason with personal convictions. The key takeaway? Even flawed ideas can contribute to intellectual progress, and pragmatism helps us understand why people believe what they do.
Final Thoughts
Pythagoras’ legacy is a testament to both the power and the pitfalls of human reasoning. His blend of empirical observation and mystical belief makes him a prime example of rational pragmatism in action.
Understanding the three types of pragmatism—empirical, rational, and irrational—helps us recognize not only how Pythagoras thought, but also how most people navigate their own belief systems. The lesson? Even great thinkers are pragmatic in their own ways, balancing what they know with what they wish were true. And that’s something we all do—whether we realize it or not.